Dirac Fields

Let

$$ \fancyscript{I} $$

I

be a subspace of an algebra

$$ \fancyscript{A} $$

A

with the property that the sum of elements in

$$ \fancyscript{I} $$

I

is also in

$$ \fancyscript{I} $$

I

:

$$ \fancyscript{I} $$

I

is called a

two-sided ideal

if it is invariant under multiplication on both the left and the right by an arbitrary element of

$$ \fancyscript{A} $$

A

:

$$ \fancyscript{I} $$

I

is called a left (right)

ideal

if it is invariant under multiplication from the

left

(right) only.